A method for determining the supplied thermal capacities to solar simulators of a thermal vacuum chamber for recreating the thermal regime of a spacecraft in the orbital flight section using the example of an infrared Fourier spectrometer is proposed. This problem is solved as a problem of minimizing the standard deviation between the incident heat flow obtained under the conditions of thermal vacuum tests and the flow simulating the conditions of orbital flight. To do this, two “direct” heat exchange problems are first solved to determine the incident heat fluxes, taking into account the diffuse re-emission between the elements. As an optimization method, the method of conjugate directions is proposed as the most accurate first-order convergence method. For it, it is necessary to determine the step of descent and the components of the gradient of the root-mean-square error. The descent step is sought from the conditions of the minimum of the target functional at each iteration, thereby regularizing our discrepancy between heat flows. The minimization problem is solved by the conjugate gradient method, which allows achieving the required convergence in the minimum number of iterations. The results show that the temperature regime of the considered spectrometer nodes correlates with the calculation in the orbital flight section.

The influence of the dose rate factor of ionizing radiation on the induction and repair efficiency of double-strand breaks (DSBs) of DNA has been studied with further prognostic analysis of the survival of human tumor cells. A549 cells have been exposed to X rays at a dose of 2 Gy at dose rates of 10 and 400 mGy/min. The degree of DNA fragmentation, immunocytochemical staining for γH2AX and RAD51 proteins and clonogenic test have been conducted. It has been found that the DNA DSB repair velocity under irradiation with a lower dose rate (10 mGy/min) is lower than that under irradiation with a high dose rate (400 mGy/min) and predominantly passes through the mechanism of homologous recombination. Other DNA DSB repair mechanisms predominate in cells irradiated at a higher dose rate (400 mGy/min). The clonogenic ability of tumor cells after irradiation with the used dose rates (10 and 400 mGy/min) decreases significantly compared with non-irradiated cells, but no significant differences have been observed between cells irradiated with different dose rates.

The generalized Korteweg–de Vries equation of an arbitrary order is considered. The equation is a generalization of the famous Korteweg–de Vries equation, the Kawahara equation, and some other equations. A theorem on the existence of solitary waves in the considered class of equations is proved. The form of a solitary wave for an equation of any order is demonstrated. Specific calculations are performed for the twelfth-order equation, for which constraints are presented on the equation parameters for the existence of solitary waves.

In the theory of functions of a complex variable, a well-known fact is the principle of maximum modulus of an analytic function of a complex variable, which states that if a function is analytic in a bounded domain and continuous on its boundary, is not a constant, then its modulus reaches its maximum value only at the points of the boundary. In the literature, this statement is proved rather cumbersome by contradiction by calculating the value of the function along a closed contour using the Cauchy integral formula. It would be interesting to obtain another, simpler proof of the principle of maximum modulus of an analytic function of a complex variable. This article provides a simpler, more rigorous proof of the maximum principle for the modulus of an analytic function of a complex variable. The modulus of a function of a complex variable is considered as a function of two variables. The proof is based on the calculation of partial derivatives of the first and second orders of the modulus of the function, the construction of a matrix of a quadratic form based on partial derivatives of the second order, and the analysis of the sign-definiteness of this form using the Sylvester criterion. It is proved that the value of the principal minor of the second order is less than zero inside the closed region and, therefore, the modulus of the function does not have an extremum.

For an arbitrary convex non-Lipchitz modulus of continuity ω(t), we construct a continuous nowhere- differentiable function ϕω(x), whose modulus of continuity does not exceed ω(t) and that has zero derivative number at every point, is constructed. This construction follows the work of B. Bolzano for the continuous nowhere-differentiable function. The function fω(z) = fω(x + iy) := ϕω(x) is a continuous nowheredifferentiable function, even if it is considered as a function of two real variables, whose modulus of continuity does not exceed ω(t) and that has zero derivative number at every point along two noncollinear directions. A sufficient condition of analyticity is obtained in this work under the assumtption that the function satisfies of the Lipschitz condition at every point ζ along some set Eζ rather than the conventional assumption that the function has a derivative with respect to z at every point ζ along some set Eζ. Such a function fω(z) shows that the former assumption cannot be weakened in this theorem.

A perturbed second-order ordinary differential equation obtained by passing to traveling wave variables in the generalized Ginzburg–Landau equation is considered. The stability of the stationary points of the equation is analyzed and intervals of parameters are found for which the system has separatrices of saddle points. Explicit expressions for the homoclinic and heteroclinic orbits of the system are found for two special cases of parameters. The stability of these orbits is analyzed t by constructing the Melnikov function along them. The analysis of the zeros of the Melnikov function allows us to determine the ranges of the control parameters of the system where the necessary condition for the occurrence of Melnikov chaos is satisfied.

Abstract—Internet of things technologies has been rapidly developed in the past decade, stimulating the development of related software products. Home Assistant is a popular home automation software. The interaction interface between Home Assistant and TouchGFX framework, which is used in the development of devices with a graphical user interface, which is based on an STM32 microcontroller, is presented in this work. The MQTT protocol, which is used to connect devices to the central server in the described system, allows the server to interact with previously known devices by using a unique identifier, which is generated when the device is connected to the system. This excludes the possibility of dynamically changing the composition of the system (adding/removing devices) without reconfiguring all interacting nodes. For this reason, it has been proposed to develop an addon for Home Assistant, which would allow devices to receive complete information on the current state of the system. To transfer received information on devices from a dynamic array to the graphical interface, real-time operating system queuing mechanisms, as well as the Model- View-Presenter design pattern, have been used. This pattern improves the scalability of the program code and simplifies the implementation of unit testing. A method has been proposed to optimize the operation of the Smart Home system under the control of the Home Assistant software.

The problem of designing a control system and optimizing parameters using a proportional–integral– derivative (PID) controller for hexapod robots, which are widely used in various fields such as dynamic simulators, robotic manipulators, and orientation systems is considered. When designing such systems, computer modeling is used, and an important issue is the creation of a simulation model of the hexapod control system and the assessment of positioning errors. A simulation model of a hexapod robot developed in the SolidWorks computer-aided design system has been reported. The hexapod robot control system has been simulated in the MATLAB software environment, which includes the Simulink library. In the process of simulation, changes in the position of the coordinates of the center of the movable platform with time, positioning errors of the hexapod rods, and forces applied to each hexapod rod in a certain period of time have been obtained at given PID controller coefficients.

The mathematical modeling of plasma-current sheath (PCS) motion in plasma focus chambers has been verified with the two-dimensional magnetohydrodynamic (MHD) code for plasma focus calculating. The operation of pulsed neutron generators based on plasma focus chambers is described. The basic MHD equations describing the behavior of a fully ionized plasma, underlying the MHD code, are also given. In the MHD code, plasma-current sheath motion is simulated in the framework of ideal one-fluid two-dimensional magnetohydrodynamics under the assumption of axisymmetric discharge development. The MHD code has been verified by comparing the calculation results with experimental data for plasma focus chambers ПФ7-02, Т19-Л316 and ПФ7-02М1 manufactured at VNIIA. The calculated values of the discharge current amplitude, the time to reach the current maximum, and the singularity time (pinching time) are compared with the respective experimental data. The program interface is shown. The experimental and calculated dependences of the discharge current amplitude on the charging voltage for the Т19-Л316 chamber are shown in the voltage range from 17 to 23 kV and currents from 150 to 200 kA. It has been concluded that this program is promising for the development of generators based on plasma-focus chambers.

A dynamic two-phase model of the pressure compensator imbalance mechanism in a nuclear power plant pressurized water reactor (PWR) has been constructed based on some reasonable simplifications and basic hypothetical assumptions. The energy and mass conservation equations are used to derive a mathematical model of the pressurizer operation. The pressurizer is divided into two regions, the vapor region and the liquid region, but not necessarily in equilibrium with each other. A model of the pressurizer control system has been developed using MATLAB/Simulink. An improved model based on the model predictive control algorithm is proposed to solve the problems of large overshoot, delayed response, and poor stability of the pressurizer pressure control system. The possibilities and potential of model predictive control (MPC) strategies for pressurizer control in nuclear power plants are studied using a linearized dynamic model of the pressurizer. The MPC controllers used are based on existing methodologies. In addition, the possibilities of improving the performance by tuning some control parameters precisely based on the dynamic characteristics of the pressurizer are investigated. The efficiency has been evaluated by means of extensive computer simulations. The results demonstrate the potential of the MPC controller to improve the performance of the pressurizer.

The use of polymer materials and composites based on them to protect against various types of radiation has become quite widespread in recent years. In this regard, the creation of new X-ray protective materials based on polymers is relevant. This work is devoted to the development of a comprehensive technique using atomic force microscopy for non-destructive quality control of X-ray self-adhesive polymer coatings. To ensure high levels of protection, filler particles should be uniformly distributed in the polymer matrix. The process of dispersion of particles in a polymer matrix is determined by the ratio of the intensities of interaction of particles with each other and with the matrix. Therefore, in order to optimize the technology and composition of the composite, it is necessary to control the uniformity of the filler distribution in the matrix, as well as to evaluate the strength of interfacial interactions. Samples based on different types of rubbers with fillers (barite, lead) have been examined on a scanning probe microscope SolverNext (NT-MDT, Zelenograd) in several modes of atomic force microscopy without changing the cantilever: topography, phase contrast, and force spectroscopy. Atomic force microscopy images have been processed using the standard ImageAnalisisP9 software. It is shown that a set of complementary modes of atomic force microscopy makes it possible to identify subtle differences in the microstructure of the composite, which is important for assessing the quality of materials using nanopowders.